## Overview

This book provides a comprehensive discussion of numerical computing techniques with an emphasis on practical applications in the fields of civil, chemical, electrical, and mechanical engineering. It features two software libraries that implement the algorithms developed in the text - a MATLAB® toolbox, and an ANSI C library. This book is intended for undergraduate students.
Each chapter includes detailed case study examples from the four engineering fields with complete solutions provided in MATLAB® and C, detailed objectives, numerous worked-out examples and illustrations, and summaries comparing the numerical techniques. Chapter problems are divided into separate analysis and computation sections. Documentation for the software is provided in text appendixes that also include a helpful review of vectors and matrices. The Instructor’s Manual includes a disk with software documentation and complete solutions to both problems and examples in the book.

## Table of Contents

1. NUMERICAL COMPUTATION

Motivation and Objectives / Number Representation / Machine Precision / Round-Off Error / Truncation Error / Random Number Generation / Numerical Software / Applications / Chapter Summary / Problems

2. LINEAR ALGEBRAIC SYSTEMS

Motivation and Objectives / Gauss-Jordan Elimination / Gaussian Elimination / LU Decomposition / Ill-Conditioned Systems / Iterative Methods / Applications / Chapter Summary / Problems

3. EIGENVALUES AND EIGENVECTORS

Motivation and Objectives / The Characteristic Polynomial / Power Methods / Jacobi’s Method / Householder Transformation / QR Method / Danilevsky’s Method / Polynomial Roots / Applications / Chapter Summary / Problems

4. CURVE FITTING

Motivation and Objectives / Interpolation / Newton’s Difference Formula / Cubic Splines / Least Square / Two-Dimensional Interpolation / Applications / Chapter Summary / Problems

5. ROOT FINDING

Motivation and Objectives / Bracketing Methods / Contraction Mapping Method / Secant Method / Muller’s Method / Newton’s Method / Polynomial Roots / Nonlinear Systems of Equations / Applications / Chapter Summary / Problems

6. OPTIMIZATION

Motivation and Objectives / Local and Global Minima / Line Searches / Steepest Descent Method / Conjugate-Gradient Method / Quasi-Newton Methods / Penalty Functions / Simulated Annealing / Applications / Chapter Summary / Problems

7. DIFFERENTIATION AND INTEGRATION

Motivation and Objectives / Numerical Differentiation / Noise-Corrupted Data / Newton-Cotes Integration Formulas / Romberg Integration / Gauss Quadrature / Improper Integrals / Multiple Integrals / Applications / Chapter Summary / Problems

8. ORDINARY DIFFERENTIAL EQUATIONS

Motivation and Objectives / Euler’s Method / Runge-Kutta Methods / Step Size Control / Multi-Step Methods / Bulirsch-Stoer Extrapolation Methods / Stiff Differential Equations / Boundary Value Problems / Applications / Summary / Problems

9. PARTIAL DIFFERENTIAL EQUATIONS

Motivation and Objectives / Elliptic Equations / One-Dimensional Parabolic Equations / Two-Dimensional Parabolic Equations / One-Dimensional Hyperbolic Equations / Two-Dimensional Hyperbolic Equations / Applications / Chapter Summary / Problems

10. DIGITAL SIGNAL PROCESSING

Motivation and Objectives / Fourier Transform / Fast Fourier Transform (FFT) / Correlation / Convolution Digital Filters / Two-Dimensional FFT / System Identification / Applications / Chapter Summary / Problems / REFERENCES AND FURTHER READING / APPENDIX 1: NLIB USING MATLAB® / A Numerical Toolbox: NLIB / Main-Program Support / Linear Algebraic Systems / Eigenvalues and Eigenvectors / Curve Fitting / Root Finding / Optimization / Differentiation and Integration / Ordinary Differential Equations / Partial Differential Equations / Digital Signal Processing / APPENDIX 2: NLIB USING C / A Numerical Library: NLIB / NLIB Data Types / NLIB Core: nlib.c / Tabular Display: show.c / Graphical Display: draw.c / Linear Algebraic Systems: linear.c / Eigenvalues and Eigenvectors: eigen.c / Curve Fitting: curves.c / Root Finding: roots.c / Optimization: optim.c / Differentiation and Integration: integ.c / Ordinary Differential Equations: ode.c / Partial Differential Equations: pde.c / Digital Signal Processing: dsp.c / APPENDIX 3: VECTORS AND MATRICES / Vector and Matrix Notation / Basic Operations / Inverses / Eigenvalues and Eigenvectors / Vector Norms / APPENDIX 4: ANSWERS TO SELECTED PROBLEMS / INDEX